Do two people who know nothing about a given topic know more, or less, than one person who knows nothing about the topic?

Andy concluded (after listening to some wild pontificating and theorizing from Tom and Ray about, believe it or not, electric cattle brakes) that it is not only possible that two know-nothings could stray further from the path of accuracy than one, but in the case of Car Talk, it’s highly likely.

Over the years, we’ve cited Andy’s letter dozens of times. But we always wondered about a couple of things.

1. What would the experts say? Is Andy’s conclusion backed up by the pros?
2. What kind of philosophical trouble has Andy gotten himself into lately?

We got answers to both these questions.

First, we posed Andy’s conundrum to a pair of philosophers, John Perry and Ken Taylor. They’re esteemed professors at the august institution of Stanford-- and with their own radio show, to boot.

Read what they had to say, then find out what Andy has been doing lately, all right here.

Ken: John, the Car Talk guys are asking our advice on one of their puzzlers. It’s a pretty famous one. They call it the Andy Question.

John: What’s the puzzle?

Ken: The question is whether two people who don't know what they are talking about know more or less, when taken together, than one person who doesn't know what he's talking about.

John: Well, that depends. When you say they don’t know what they are talking about, do you really mean that literally – they know absolutely nothing about the subject matter at hand?

Ken: It’s pretty hard to imagine somebody talking at any length about something they know absolutely nothing about. Where would they even begin? But I’ll play along. Suppose we’ve got two people discussing a topic about which neither knows a lick.

John: Well, then it’s a matter of simple arithmetic. One person who knows nothing about a topic knows zero, zilch, nada about it. Two people who know nothing about the same topic, each knows zero. Add zero to zero and you get zero. So two people who know nothing about a topic know exactly as much – namely zero – as one person who knows nothing about it. Case closed.

Ken: Not so fast. You made a faulty assumption there. Usually when we say a person doesn’t know what she is talking about, we don’t really mean that she knows absolute nothing. She may know a little bit.

John: A little bit of knowledge is a dangerous thing, Ken.

Ken: The issue that got this all started had to do with electric brakes on a cattle carrier. Click and Clack may not have known much about electric brakes and cattle cars, but surely they knew something – like if there were electric brakes, they would be electric.

John: You don’t have to be a genius to figure that out. Everybody knows that sort of thing.

Ken: My point is that as soon as you let each of our know-nothings have even just the tiniest bit of knowledge about their subject, things change dramatically.

John: I don’t really see how.

Ken: Think of in terms of possibilities. Knowledge excludes possibilities. If you don’t know whether Hillary will run in 2016 or not, then, as far as you know, there are two possibilities: that she will and that she won’t. If you learn which she will do, you eliminate one possibility. The less you know, the more possibilities left open.

John: But how does this help us with the Andy question?

Ken: Well, just for the sake of argument suppose that I know almost nothing about the philosopher Malebranche. If we list 1000 yes/no questions about Malebranche, there are 2000 possibilities. If I know only ten answers, there are 1990 possibilities left.

John: Okay, I’m with you so far.

Ken: Now suppose you are just as ignorant as me… but in a different way. As long as your ten answers and my ten answers don’t overlap, between us we can eliminate twenty possibilities. So, you see, it follows that two people who know (next to) nothing about a topic, may still know more than one person who knows (next to nothing) about it.

John: But you’ve got it all backwards. Suppose you know that Malebranche had bad gas. But I not only don’t know that, I have grave doubts that this is so.

Ken: Well, if I know it, you must be wrong. Nobody can know what isn’t true.

John: Well, okay, but answer me this: if you know something – really know it – then you don’t have doubts, do you?

Ken: Couldn’t I be absolutely certain of something, but still not know it? I don't want to name any names, but I’ve met plenty of blowhard ignoramuses who think they know everything, but in reality don’t know anything at all.

John: Well one problem with those blowhard ignoramuses is that they are totally immune to self-doubt. You’re not like that, are you Ken?

Ken: I try not to be.

John: So what’s going to happen to your confidence that Malebranche had such bad gas, when you are confronted by my doubts? You going to stubbornly stick to your guns, or are you going to open your mind to the possibility that you might be wrong?

Ken: Well, you know, I never really met the guy. I’m not even sure where I got the idea that he was full of flatulence.

John: So put the two of us together and what happens? Doubt multiplies. That means that fewer possibilities are ruled out. And that means that knowledge diminishes. In other words, taken together, we know less about Malebranche’s flatulence than either of us did on his own.

Ken: But wait a minute, why are you assuming that when we pool our knowledge and our ignorance, ignorance will persist at the group level and knowledge will diminish?

John: Have you ever known invincible ignorance to just wither away when confronted with genuine knowledge?

Ken: I refuse to believe that knowledge can be driven out by ignorance. In fact, I think human flourishing depends on each of us contributing the little bits that we know to a group that knows more than any of us ever could know on our own.

John: I hate to call you naïve, Ken. So I won’t. But I will say that you radically underestimate the power of the ignorant to shout the knowledgeable down. It’s a problem as old as Socrates and the Sophist. Unfortunately I doubt it’s ever going away.

Thanks, John and Ken. We know Andy will sleep better, too, knowing that his conclusion hasn’t been found to be riddled with philosophical bullet holes!

As for what Andy’s up to these days, we managed to track him down at his Center for the Contemplation of Philosophical Conundrums as Posed by Talk Show Hosts, where he has acheived Guru status in the Department of Armchair Philosophy. What’s he up to? Well...

Car Talk: How has your life changed since the public humiliation of being associated with our lousy show?

Andy: I know you’re going to find this hard to believe, but I got newfound respect from many of my neighbors. They tend to be Car Talk types-- people are somewhat entertainment starved here in the sticks. Strangers occasionally freak out when they discover I’m THAT Andy, I hear from long lost friends every time the letter airs. The first time it aired I almost lost my sister, as she nearly drove off the road when she heard my name on the show.

Car Talk: Glad we dodged the fratricide charge! Have you written any more epic letters to other public figures since then?

Andy: One other epic letter, to the New York Times on a serious subject, but apparently it's quite hard to get one accepted by the Times. As opposed to getting on Car Talk. Just sayin’.

Car Talk: Anyone who’s ever had a letter read on Car Talk, automatically gets rejected from the NY Times on principle. So how has this profound understanding changed your life? Do you find yourself unwilling to trust two morons together?

Andy: One benefit of the letter airing is that often all I have to say is “If two people…..” and because of the notoriety of the hypothesis, the dingbats immediately stop conjecturing. [Car Talk Editorial Aside: We can think of two dingbats who continue to conjecture.] Another benefit is that, at times, I’m one of the dingbats and I catch myself more quickly, thereby minimizing the depth of the malarky we were wading into.

Car Talk: We marvel at your self-restraint.

Andy: There was tremendous satisfaction in having the question answered by Click and Clack because we had struggled for years trying to make a definitive determination. They completely and unequivocally cleared it up.

Car Talk: Glad we could help. Anything else you wanted to mention, before we wrap this up?

Andy: As a matter of fact, yes. Where are people located before they are born and does one return to that place in the end?

Car Talk: Whoa. You’re still thinking, aren’t you? That’s over our pay grade. But if you have a car problem, you know where to reach us. Thanks Andy!